Main assumptions
Closure
No false positives
Independence of occurrence and detection: occupancy status at one site should be independent of the occupancy status at another site (except for what we can explain with covariates). Detection probability should also be independent across repeated visits.
Homogeneity of detection process: unexplained variation in detection can cause underestimates in occupancy (use covariates)
Parametric assumptions: we assume that our statistical models (typically with covariates) are a reasonable abstraction of reality.